However, we don't want the slope of the tangent line at just any point but rather specifically at the point. And so this is the same thing as three plus positive one, and so this is equal to one fourth and so the equation of our line is going to be Y is equal to one fourth X plus B. So three times one squared which is three, minus X, when Y is one, X is negative one, or when X is negative one, Y is one.
Solve the equation as in terms of. Equation for tangent line. Simplify the expression. Multiply the exponents in. The final answer is the combination of both solutions. Step-by-step explanation: Since (1, 1) lies on the curve it must satisfy it hence. Move to the left of. Apply the product rule to.
The equation of the tangent line at depends on the derivative at that point and the function value. By the Sum Rule, the derivative of with respect to is. Move all terms not containing to the right side of the equation. Our choices are quite limited, as the only point on the tangent line that we know is the point where it intersects our original graph, namely the point. Factor the perfect power out of. Now find the y-coordinate where x is 2 by plugging in 2 to the original equation: To write the equation, start in point-slope form and then use algebra to get it into slope-intercept like the answer choices. Consider the curve given by xy 2 x 3y 6 18. That's what it has in common with the curve and so why is equal to one when X is equal to negative one, plus B and so we have one is equal to negative one fourth plus B. The derivative is zero, so the tangent line will be horizontal. Using all the values we have obtained we get. Now, we must realize that the slope of the line tangent to the curve at the given point is equivalent to the derivative at the point. Simplify the result. So one over three Y squared. First, find the slope of the tangent line by taking the first derivative: To finish determining the slope, plug in the x-value, 2: the slope is 6.
Substitute the values,, and into the quadratic formula and solve for. Distribute the -5. add to both sides. Rewrite in slope-intercept form,, to determine the slope. Write an equation for the line tangent to the curve at the point negative one comma one. Consider the curve given by xy 2 x 3y 6 4. All right, so we can figure out the equation for the line if we know the slope of the line and we know a point that it goes through so that should be enough to figure out the equation of the line. We now need a point on our tangent line. Given a function, find the equation of the tangent line at point. Your final answer could be. Set the numerator equal to zero. Yes, and on the AP Exam you wouldn't even need to simplify the equation.
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